Failure criteria for isotropic bodies revisited

Existing failure criteria for isotropic bodies are reconsidered and compared with modern versions, taking into account either the influence of the strength differential effect or the influence of the internal dilation of the materials on yielding and, therefore, the contribution of the hydrostatic component of stress in failure. Modern criteria are expressed by quadric polynomials whose coefficients constitute convenient terms of the failure tensor of the material which for the isotropic body is defined by the respective failure stresses in simple tension and compression.